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Edray Herbert Goins, Teoría De Números, Geometría Algebraica

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Edray Herbert Goins, Teoría De Números, Geometría Algebraica MATEMÁTICOS ACTUALES Edray Herbert Goins, Teoría de números, geometría algebraica Edray Herber Goins nació en el centro-sur de Los Ángeles y, teniendo en cuenta el reconocimiento que figura en el encabezamiento de su tesis, este matemático parece haber sido orientado por su madre, Eddi Beatrice Goins, y también por su padrino, William Herber Dailey. Él escribe esto: Al autor le gustaría dar el máximo crédito a su madre, Eddi Beatrice Goins, y a su padrino, William Herber Dailey, por su constante orientación, apoyo y protección a lo largo de los años. Edray Goins fue criado junto con su hermano. Del resumen de la charla “Black Mathematician: My Journey from South Central to Studying Dessins d'Enfants” que dio en 2015 en la Universidad de Michigan, en el "Coloquio del Dr. Marjorie Lee Browne" obtenemos los siguientes detalles. En 1939, Annie Beatrice Brown dio a luz en Marshall, Texas, a Eddi Beatrice Brown. Pasó la mayoría de los años 1936- 1942 tomando clases de educación en Bishop College, alternando su tiempo entre tomar clases de educación y ser una madre que se queda en casa. Eddi Beatrice Brown se convirtió en maestra, se casó con Goins, y en 1972 dio a luz a Edray Herber Goins, el protagonista de esta biografía, en el centro-sur de Los Ángeles. Edray siempre ha dicho que su madre y otros maestros en el sistema de Escuelas Públicas Unificadas de Los Ángeles, a las que él asistió, le alentaron y motivaron a estudiar mucho y asumir desafíos de aprendizaje adicionales [Referencia 9]: Incluso a temprana edad, Edray mostraba sed de conocimientos. Pidió a sus maestros que lo dejaran estudiar con anticipación, o bien conocer asignaturas que no formaban parte del plan de estudios. Tuvo mucho éxito en la escuela secundaria y en 1989 ganó la Medalla de Bronce en Matemáticas del Decathlon Académico de Los Ángeles. La prueba preliminar de evaluación escolar en el momento en que Goins estaba en la escuela secundaria consistía en una sección de matemáticas y una sección verbal. La National Merit Scholarship Corporation estableció el Programa Nacional de Becas de Logro en 1964 que tiene como objetivo reconocer a los estudiantes negros destacados de la educación secundaria de los Estados Unidos. Los estudiantes negros pueden ingresar tanto en este programa como en el programa National Merit al realizar el Examen Preliminar de Evaluación Escolar. En 1989, a Goins se le otorgó una Mención de Honor de la National Merit Scholarship, y al año siguiente se graduó en el High School y recibió una National Achievement Scholarship. Esta no fue la única beca que recibió antes de ingresar al Instituto de Tecnología de California, Pasadena, California, ya que en 1990 también recibió una beca Roy A Wilkins de la Asociación Nacional para el Avance de las Personas de Color, una beca Sigma Pi Phi y un Robert A Millikan Physics Scholarship del Instituto de Tecnología de California. En el Instituto de Tecnología de California se dio cuenta rápidamente de que quería ser investigador de matemáticas. Él dijo [Referencia 4]: 1 Sabía desde una etapa bastante temprana de mi vida, desde mi primer año de universidad para ser exactos, que quería ser matemático de investigación. Mostró sus habilidades desde su primer año, recibiendo el Premio Morgan Ward de Matemáticas tanto en 1991 como en 1992. El Instituto de Tecnología de California brinda la siguiente información sobre este premio: El Premio Morgan Ward fue establecido por el Departamento de Matemáticas en 1963 para honrar la memoria del profesor Morgan Ward en reconocimiento a su largo servicio a las matemáticas y al Instituto. La competencia está abierta a todos los estudiantes de primero y segundo año, independientemente de los principales. Una entrada consiste en un problema matemático junto con una solución o una contribución significativa hacia una solución. ... La solución al problema puede tener cualquier fuente, pero esta fuente debe indicarse en la entrada. Las entradas pueden juzgarse en función de la naturaleza del problema, la originalidad y la elegancia de la solución. También ganó una beca de la American Physical Society de 1991-92. En Physics Today (noviembre de 1991) se dan detalles de estas becas: La American Physical Society ha otorgado becas patrocinadas por empresas para el año académico 1991-92 a 22 estudiantes minoritarios que se especializan en física. ... Las becas se otorgan a estudiantes afroamericanos, hispanos o nativos americanos que son estudiantes de último año de secundaria o estudiantes de primer año o segundo año de universidad. Las selecciones se basan en calificaciones académicas y logros, declaraciones personales ... y cartas de referencia. Cada beca consta de 2000 dólares, que se pueden usar para matrícula, alojamiento y comida, y se pueden renovar una vez. De hecho, la beca de la American Physical Society de Goins se renovó para el año 1992-93. También en 1993 se le otorgó una beca de la Fundación Filantrópica de Los Ángeles que es para estudiantes que necesitan ayuda financiera y participan en actividades escolares extracurriculares y servicio comunitario. En el Instituto de Tecnología de California, Goins fue asesorado por el profesor de matemáticas Dinakar Ramakrishnan y el profesor de física teórica Steven C Frautschi. En junio de 1994, Goins se graduó con un B.S. especializándose en Matemáticas y Física. Había ganado varios premios durante sus años de pregrado en el Instituto de Tecnología de California, a saber, la Dean's Cup for Service (1993), el Doris S Perpall Speaking Award a la mejor presentación en Humanities (1993) y el Rodman W Paul History Prize (1994). En 1994, Goins recibió una Beca de Investigación de Graduados de la Fundación Nacional de Ciencias (Mención de Honor) y una Beca de Graduados del Consorcio Nacional de Ciencias Físicas que le permitió comenzar la investigación para un doctorado. en la universidad de Stanford. Durante los veranos de 1995 y 1996 realizó una pasantía de verano de junio a agosto en la Agencia de Seguridad Nacional, Fort George Meade, Maryland. En 1996 se le otorgó el Premio al Estudiante Graduado Sobresaliente del Centro de Servicios Comunitarios Black, Universidad de Stanford. Sus asesores de tesis en Stanford fueron Daniel Willis Bump y Karl Cooper Rubin. En 1999 recibió una serie de premios y honores de la Universidad de Stanford por sus destacadas contribuciones: el Premio James W Lyons al Servicio, Universidad de Stanford; el Premio al Servicio de Graduados, Consejo de Estudiantes Graduados, Universidad de Stanford; y el destacado estudiante de posgrado, Asociación de Estudiantes de Posgrado Chicano/Latino, 2 Universidad de Stanford. Obtuvo el doctorado (Ph.D.) en septiembre de 1999 por su tesis Curvas elípticas y representaciones icosaédricas de Galois. Goins da los siguientes reconocimientos en su tesis: El autor desea agradecer a su asesor, Dan Bump, por sugerir el problema original; su co-asesor no oficial Karl Rubin por sus invaluables sugerencias y la comprensión de que la curva elíptica es isógena a su conjugado; y al estudiante graduado William Stein por su ayuda en el cálculo de coeficientes a través del algoritmo de símbolo modular de Cremona. Esta tesis no podría haberse completado sin su ayuda. El autor también quisiera agradecer a las siguientes personas por conversaciones útiles: David Carlton, Jordan Ellenberg, Ralph Greenburg, Kenneth Ribet y Richard Taylor. Los documentos de Ki-ichiro Hashimoto y Yuji Hasegawa también fueron útiles para obtener información sobre las propiedades de las curvas Q. Toda la investigación fue patrocinada por una beca generosa del Consorcio Nacional de Ciencias Físicas (NSPC) y la Agencia de Seguridad Nacional (NSA). Aunque la fecha en que presentó su Ph.D. La tesis se muestra claramente en una copia en la web como "agosto de 1999" y "Copyright por Edray Herber Goins 1999", la Universidad de Stanford tiene una copia de la tesis en su sitio web con fecha "octubre de 2002" y tiene "Copyright por Edray Herber Goins 2003". Esto es desconcertante, pero la fecha de 1999 seguramente es correcta, ya que esa copia tiene las firmas de los examinadores, mientras que la copia de 2002 no. En su tesis, Goins examinó los casos de la Conjetura de Artin y presenta los antecedentes al comienzo de la tesis: En 1917, Erich Hecke probó una serie de resultados sobre ciertos caracteres que ahora se conocen comúnmente como caracteres de Hecke; un coro- lario establece que las representacio- nes complejas unidimensionales de Galois dan lugar a toda la serie L. Reveló, a través de una serie de con- ferencias en el Instituto de Estudios Avanzados de Princeton en los años si- guientes, la relación entre representa- ciones tales como generalizaciones de caracteres de Dirichlet y formas mo- dulares como las funciones propias de un conjunto de operadores de conmu- tación autoadjuntos. Muchos matemá- ticos se inspiraron en su visión innovadora y su novedosa prueba de la continuación analítica de la serie L y su ecuación funcional. En la década de 1930, Emil Artin conjeturó que una generalización de tal resultado debería ser cierta; es decir, las representaciones proyectivas complejas irreducibles de grupos de Galois finitos también deberían dar lugar a toda la serie L. Llegó a esta conclusión después de probarse a sí mismo que tanto las representaciones tridimensionales como las 4 dimensiones del grupo simple de orden 60, el grupo alterno A5, dan lugar a la serie L con singularidades. En el espíritu de Hecke, formuló su conjetura en términos de la continuación analítica de la serie L y su ecuación funcional. Es sabido, debido a la percepción de Robert Langlands en la década de 1970 que relaciona los caracteres de Hecke con la teoría de la representación, que para probar la conjetura es suficiente demostrar que tales representaciones son automorfas.
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